1.6 Conversion tables for units
The table below gives conversion factors from a variety of units to the corresponding SI unit.
Examples of the use of this table have already been given in the preceding section. For each
physical quantity the name is given, followed by the recommended symbol(s). The SI unit is
given, followed by the esu, emu, Gaussian unit (Gau), atomic unit (au), and other units in
common use, with their conversion factors to SI. The constant ζ which occurs in some of the
10
-1
electromagnetic conversiton factors is the (exact) pure number 2.997 924 58×10 = c0/(cm s ).
The inclusion of non-SI units in this table should not be taken to imply that their use is to be
encouraged. With some exceptions, SI units are always to be preferred to non-SI units.
However, since may of the units below are to be found in the scientific literature, it is
convenient to tabulate their relation to the SI.
For convenience units in the esu and Gaussian systems are quoted in terms of the four
dimensions length, mass, time, and electric charge, by including the franklin (Fr) as an
abbreviation for the electrostatic unit of charge and 4πε0 as a constant with dimensions
2
(charge) /(energy×length). This gives each physical quantity the same dimensions in all
systems, so that all conversion factors are pure numbers. The factors 4πε0 and the Fr may be
½
½
3/2 ½ -1
ir)
2
-1
eliminated by writing Fr = esu of charge = erg cm = cm g s , and 4πε0 = ε = 1 Fr erg
-1
cm = 1, to recover esu expressions in terms of three base units (see section 7.3 below). The
symbol Fr should be regarded as a compact representation of (esu of charge).
Conversion factors are either given exactly (when the = sign is used), or they are given to the
approximation that the corresponding physical constants are known (when the ≈ sign is used). In
the latter case the uncertainty is always less than ±5 in the last digit quoted.
Chapter 1 - 1
Name
length, l
metre (SI unit)
centimetre (cgs unit)
ångström
micron
millimicron
x unit
fermi
inch
foot
yard
mile
nautical mile
astronomical unit
parsec
light year
light second
area, A
square metre (SI unit)
barn
acre
are
hectare
volume, V
cubic metre (SI unit)
litre
lambda
barrel (US)
gallon (US)
gallon (UK)
Symbol
m
cm
Å
µ
mµ
X
f, fm
in
ft
yd
mi
AU
pc
l.y.
Relation to SI
-2
= 10 m
-10
= 10 m
-6
= µm = 10 m
-9
= nm = 10 m
-13
≈ 1.002×10 m
-15
= fm = 10 m
-2
= 2.54×10 m
= 12 in = 0.3048 m
= 3 ft = 0.9144 m
= 1760 yd = 1609.344 m
= 1852 m
11
= 1.496 00×10 m
16
≈ 3.085 68×10 m
15
≈ 9.460 528×10 m
= 299 792 458 m
2
m
b
-28
2
= 10 m
2
≈ 4046.856 m
2
= 100 m
4
2
= 10 m
a
ha
3
m
l, L
λ
3
gal (US)
gal (UK)
Chapter 1 - 2
-3
3
= dm = 10 m
-6
3
= µl = 10 dm
3
≈ 158.987 dm
3
= 3.785 41 dm
3
= 4.546 09 dm
Name
Symbol
mass, m
kilogram (SI unit)
gram (cgs unit)
electron mass (au)
unified atomic mass
unit, daltonS
gamma
tonne
pound (avoirdupois)
ounce (avoirdupois)
ounce (troy)
grain
time, t
second (SI, cgs unit)
au of time
minute
hour
1
day
2
year
svedberg
Relation to SI
kg
g
me
u, Da
= 10 kg
-31
≈ 9.109 39×10 kg
12
-27
= ma( C)/12 ≈ 1.660 540×10 kg
γ
t
lb
oz
oz (trou)
gr
= µg
3
= Mg = 10 kg
= 0.453 592 37 kg
≈ 28.3495 g
≈ 31.1035 g
= 64.798 91 mg
s
h/Eh
min
h
d
a
Sv
≈ 2.418 88×10
= 60 s
= 3600 s
= 86 400 s
≈ 31 556 952 s
-13
= 10 s
-3
-17
s
(1)
Note that the day is not exactly in terms of the second since so-called leap-seconds are
added or subtracted from the day semiannually in order to keep the annual average
occurrence of midnight at 24:00 on the clock.
(2)
The year is not commensurable with the day and not a constant. Prior to 1967, when the
atomic standard was introduced, the tropical year 1900 served as the basis for the
definition of the second. For the epoch 1900.0. it amounted to 365.242 198 79 d ≈ 31
556 925.975 s and it decreases by 0.530 seconds per century. The calendar years are
exactly defined in terms of the day:
Julian year = 365.25 d
Gregorian year = 365.2425 d.
The definition in the table corresponds to the Gregorian year. This is an average based
on a year of length 365 days, with leap years of 366 days; leap years are taken either
when the year is divisible by 4 but is not divisible by 100, or when the year is divisible
by 400. Whether the year 3200 should be a leap year is still open, but this does not have
to be resolved until sometime in the middle of the 32nd century.
Chapter 1 - 3
Name
Symbol
Relation to SI
acceleration, a
SI unit
standard acceleration of
free fall
gal, galileo
ms
gn
= 9.806 65 m s
Gal
= 10 m s
force, F
3
newton (SI unit)
dyne (cgs unit)
au of force
kilogram-force
N
dyn
Eh/a0
kgf
= kg m s
-2
-5
= g cm s = 10 N
-8
≈ 8.238 73×10 N
= 9.806 65 N
energy, U
joule (SI unit)
erg (cgs unit)
rydberg
electronvolt
calorie, thermochemical
calorie, international
15 °C calorie
litre atmosphere
British thermal unit
J
erg
Ry
eV
calth
calIT
cal15
l atm
Btu
= kg m s
2 -2
-7
= g cm s = 10 J
-18
= Eh/2 ≈ 2.179 87×10 J
-19
= e×V ≈ 1.602 18×10 J
= 4.184 J
= 4.1868 J
≈ 4.1855 J
= 101.325 J
= 1055.06 J
Pa
atm
bar
Torr
mmHg
= N m = kg m s
= 101 325 Pa
5
= 10 Pa
= (101 325/760) Pa ≈ 133.322 Pa
-2
= 13.5951×980.665×10 Pa ≈ 133.322 Pa
psi
≈ 6.894 757×10 Pa
W
hp
= kg m s
= 745.7 W
pressure, p
pascal (SI unit)
atmosphere
bar
torr
millimetre of mercury
(conventional)
pounds per squere inch
power, P
watt (SI unit)
horse power
(3)
-2
-2
-2
-2
-2
2 -2
-2
-1 -2
3
2 -3
1 N is approximately the force exerted by the earth upon an apple.
Chapter 1 - 4
Name
Symbol
Relation to SI
action, L, J (angular momentum)
SI unit
cgs unit
au of action
JS
erg s
h = h / 2π
= kg m s
-7
= 10 J s
-34
≈ 1.054 57×10 J s
dynamic viscosity, η
SI unit
poise
centipoise
Pa s
P
cP
= kg m s
-1
= 10 Pa s
= mPa s
kinematic viscosity, v
SI unit
stokes
m s
St
= 10 m s
thermodynamic temperature, T
kelvin (SI unit)
4
degree Rankine
K
°R
= (5/9) K
entropy, S
heat capacity, C
SI unit
clausius
JK
Cl
molar entropy, Sm
molar heat capacity, Cm
SI unit
entropy unit
(4)
2 -1
-1 -1
2 -1
-4
2 -1
-1
-1
= calth/K = 4.184 J K
-1
-1
J K mol
e.u.
-1
-1
-1
-1
= calth K mol = 4.184 J K mol
T/°R = (9/5) T/K. Also, Celsius temperature θ is related to thermodynamic temperature
T by equation
θ/°C = T/K - 273.15
Similarly Fahrenheit temperature θF is related to Celsius temperature θ by the equation
θF/°F = (9/5) (θ/°C) + 32
Chapter 1 - 5
Name
Symbol
molar volume, Vm
SI unit
amagat
m mol
amagat
plane angle, α
radian (SI unit)
degree
minute
second
grade
rad
°
′
″
grad
= rad×2π/360 ≈ (1/57.295 78) rad
= degree/60
= degree/3600
= rad×2π/400 ≈ (1/63.661 98) rad
radioactivity, A
becquerel (SI unit)
curie
Bq
Ci
=s
10
= 3.7×10 Bq
absorbed dose of radiation
gray (SI unit)
rad
Gy
rad
= J kg
= 0.01 Gy
dose equialent
sievert (SI unit)
rem
Sv
rem
= J kg
≈ 0.01 Sv
3
Relation to SI
-1
= Vm of real gas at 1 atm and 273.15 K
-3
3
-1
≈ 22.4×10 m mol
-1
5
(5)
-1
-1
The unit röntgen, employed to express exposure to X or γ radiation, is equal to: R =
-4
-1
2.58 x 10 C kg
Chapter 1 - 6
Name
Symbol
Relation to SI
electric current, I
ampere (SI unit)
esu, Gau
biot (emu)
A
(10/ζ)A
Bi
≈ 3.335 64×10
= 10 A
electric charge, Q
coulomb (SI unit)
franklin (esu, Gau)
emu (abcoulomb)
proton charge (au)
charge density, ρ
SI unit
esu, Gau
electrical potential, V, φ
volt (SI unit)
esu, Gau
mean international volt
US international volt
electric resistance, R
ohm (SI unit)
mean international ohm
US international ohm
C
Fr
-10
A
=As
-10
= (10/ζ)C ≈3.335 64×10 C
= 10 C
-19
-10
≈ 1.602 18×10 C ≈ 4.803 21×10 Fr
e
-3
Cm
-3
Fr cm
7 -1
-3
-4
-3
= 10 ζ C m ≈ 3.335 64×10 C m
-1
-1 -1
V
-1
erg Fr
=JC =JA s
-1
= Fr cm /4πε0 = 299.792 458 V
= 1.00034 V
= 1.000 330 V
Ω
= V A = m kg s A
= 1.000 49 Ω
= 1.000 495 Ω
-1
2
-3
-2
electric field, E
SI unit
esu, Gau
Vm
=JC m
-2
4
-1
Fr cm /4πε0 = 2.997 924 58×10 V m
electric field gradient, Eβ, qαβ
SI unit
esu, Gau
Vm
=JC m
-3
6
-2
Fr cm /4πε0 = 2.997 924 58×10 V m
electric dipol moment, p, µ
SI unit
esu, Gau
debye
Cm
Fr cm
D
-1
-1
-1
-2
-1
-2
-12
≈ 3.335 64×10 C m
-18
-30
= 10 Fr cm ≈ 3.335 64×10 C m
Chapter 1 - 7
Name
Symbol
Relation to SI
electric quadrupole moment,
Qαβ, Θαβ, eQ
2
SI unit
Cm
2
esu, Gau
Fr cm
≈ 3.335 64×10
magnetic flux density, B
(magnetic field)
tesla (SI unit)
gauss (emu, Gau)
T
G
= J A m = V s m = Wb m
-4
= 10 T
magnetic flux, Φ
weber (SI unit)
maxwell (emu, Gau)
Wb
Mx
=JA =Vs
-2
-8
= G cm = 10 Wb
-14
-1
-2
-2
Cm
-2
-2
-1
magnetic field, H
(volume) magnetization, M
-1
-1
-1
=Cs m
SI unit
Am
3
-1
oersted (emu, Gau)
Oe
= 10 A m
(ir)
[But note: in practice the oersted, Oe, is only used as a unit for H = 4πH; thus when
(ir)
3
-1
H = 1 Oe, H = (10 /4π) A m .]
magnetic dipole moment, m, µ
2
SI unit
Am
-1
emu, Gau
erg G
6
Bohr magneton
µB
nuclear magneton
µN
=JT
2
-3
-1
= 10 A cm =10 J T
-24
-1
= eh/2me ≈ 9.274 02×10 J T
-27
-1
= (me/mp)µB ≈ 5.050 79×10 J T
magnetizability, ξ
SI unit
= C m kg
(6)
-2
JT
-1
2
2
-1
The Bohr magneton µB is sometimes denoted BM (or B.M.), but this is not
recommended.
Chapter 1 - 8
Name
Symbol
Relation to SI
magnetic susceptibility, χ, κ
SI unit
1
emu, Gau
1
[But note: in practice susceptibilities quoted in the context of emu or Gaussian units are
(ir)
(ir)
-6
-6
always values for χ = χ/4π; thus when χ = 10 , χ = 4π×10 .]
molar magnetic susceptibility, χm
3
-1
SI unit
m mol
3
-1
-6
3
-1
emu, Gau
cm mol
= 10 m mol
3
-1
[But note: in practice the units cm mol usually imply that the irrational molar
(ir)
(ir)
-6
3
susceptibility is being quoted, χm = χm/4π; thus, for example if χm = -15×10 cm
-1
-10
3
-1
mol , which is often written as '-15 cgs ppm', then χm = -1.88×10 m mol .]
Chapter 1 - 9